Problem:
A derivative security of European style with expiration in 1 year has this payoff: max(0, min(3K-S, S-K)), where K = 10 is the strike price and S is the price of the underlying stock at expiration. The stock currently trades at 25, and the following prices for European options on the stock are known (all expiring in 1 year).
| Type | Strike | Price |
| Call |
10 |
16.76 |
| Call |
20 |
7.02 |
| Put |
10 |
0.85 |
| Put |
30 |
6.05 |
Requirement:
Question 1: Draw a graph of the payoff as a function of S
Question 2: What is the 1 year interest rate r?
Question 3: What is the price P of the derivative security?
Note: Please show basic calculation